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David Burr, Guido Marco Cicchini, Givanni Anobile; Mapping number to space engages adaptive encoding mechanisms . Journal of Vision 2014;14(10):1423. doi: 10.1167/14.10.1423.
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© ARVO (1962-2015); The Authors (2016-present)
The mapping of number onto space is fundamental to measurement and mathematics. However, number mapping of young children, unschooled adults and adults under attentional load show strong compressive non-linearities, thought to reflect intrinsic logarithmic encoding mechanisms, which are "linearized" by education. Here we advance and test an alternative explanation: that the non-linearity results from adaptive Bayesian mechanisms (akin to a Kalman filter), which take into account the statistics of recent stimuli. This theory predicts that the response to the current trial should correlate positively with the magnitude of the previous trial: whereas a static logarithmic non-linearity predicts trial-wise independence. Consistent with predictions, we found strong and highly significant correlations between numberline mapping of the current trial and the magnitude of previous trials, in both adults and school children. The dependency is sufficient to account for the shape of the numberline (using a simple, one-parameter model), without recourse to static non-linearities such as logarithmic encoding. Simulations show that this dynamic strategy is efficient, resulting in a reduction of overall reproduction error, and may well reflect a general strategy to cope adaptively with environmental statistics.
Meeting abstract presented at VSS 2014
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